Measuring stellar differential rotation with high-precision space-borne photometry

Abstract

Context. Stellar differential rotation is important for understanding hydromagnetic stellar dynamos, instabilities, and transport processes in stellar interiors, as well as for a better treatment of tides in close binary and star-planet systems. Aims. We introduce a method of measuring a lower limit to the amplitude of surface differential rotation from high-precision, evenly sampled photometric time series, such as those obtained by space-borne telescopes. It is designed to be applied to main-sequence late-type stars whose optical flux modulation is dominated by starspots.Methods. An autocorrelation of the time series was used to select stars that allow an accurate determination of starspot rotation periods. A simple two-spot model was applied together with a Bayesian information criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty were obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov chain approach. We applied our method to the Sun and eight other stars for which previous spot modelling had been performed to compare our results with previous ones. Results. We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite for successfully measuring differential rotation through spot modelling. For a proper Monte Carlo Markov chain analysis, it is necessary to take the strong correlations among different parameters that exist in spot modelling into account. For the planet-hosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation of ΔP/P = 0.0523± 0.0016. We confirm that the Sun as a star in the optical passband is not suitable for measuring differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison to more sophisticated and time-consuming approaches.

The variability behaviour of CoRoT M-giant stars

“…Here we only consider stars with V-, I-, J-, and K S -band photometry. We note that the reddening may not only be caused by interstellar, but also by circumstellar reddening (Lebzelter 2011) The corrected colours show a reasonable agreement with the empirical calibrations of Worthey & Lee (2011). However, there are two groups of stars that do not follow this trend.…”

“…A total of 434 stars were found with previously determined periods (Lebzelter 2011;De Medeiros et al 2013). For approximately 96% of the targets, the differences between our periods and those periods of the other authors are less than 10%.…”

“…However, these events have not been confirmed in recent studies (e.g., Mais et al 2004;Woźniak et al 2004;Lebzelter 2011;Hartig et al 2014). Indeed, using data from CoRoT and Kepler, Lebzelter (2011) and Hartig et al (2014) do not confirm such variations, despite photometric precisions of a few mmag. Therefore, the observed short-time variations are very rare or not physical.…”

“…(MacConnell 1988;Stephenson 1989Stephenson , 1996Alksnis et al 2001;Chen & Yang 2012;Zacharias et al 2013). We also cross-checked with previous studies using CoRoT data (Lebzelter 2011;Sebastian et al 2012;Guenther et al 2012;Sarro et al 2013;De Medeiros et al 2013). Finally, we also searched in many other databases incorporated in the International Virtual Observatory Alliance 3 , using the Tool for OPerations on Catalogues And Tables (TOPCAT 4 - Taylor 2005).…”

“…Full Tables 2-4 are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/583/A122 of surface differential rotation (Lanza et al 2014), and the detection of eclipsing binary systems (e.g., Maceroni et al 2009;Slawson et al 2011;Maciel et al 2011). The aforementioned science cases represent only a few of the major topics among the many aspects of time-domain, high-precision photometry.…”